Only my second day (and about 4 hours) playing this, and I'm loving it.
You look at the icons in the sector you are jumping to. Also, the map will show you what ships are in the adjacent sectors and if/where they are jumping.
Also, selecting the right quadrant of the sector to jump to can make a HUGE difference in the outcome of the battle.
I am still on the basic ship, and completed the first 'galaxy' quest. I just took my time, fought very conservatively, built up credits and upgrades until I had a good fleet before going after ANY of the main bad guys.
WIith the base carrier, and 2 BSE Ravagers, I was able to go through the map.
Upgrade to the bombers when you can, and upgrading their 'burst' seems to be the most effective (and get all 4). Put missiles on your support ships, maximize their range, with the point defense you should be able to take anything on the first map.
The trick is to warp in far from your target, take out all of the support craft before closing to range. Some targets will continuously generate fighters (like your carrier does), you can mostly ignore them unless they have standoff weapons, then you'll have to send your fighters to take them out.
Once all the support ships are gone, you can move into range of your missiles and long range turrets until you simply overwhelm their defenses.